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Regionalizing Stochastic Rainfall Generators

The study presented at the World Environmental & Water Resources Congress 2010 outlines the use of stochastic rainfall generators, specifically the MBLRP model, to simulate rainfall data in regions with limited or missing monitoring equipment. The research demonstrates regionalization of rainfall parameters across the contiguous U.S. using Ordinary Kriging interpolation and cross-validation techniques. Findings indicate significant variability in storm characteristics, which can assist in assessing risks related to hydrologic phenomena such as floods and droughts.

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Regionalizing Stochastic Rainfall Generators

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  1. American Society Civil Engineers Environmental and Water Resources Institute World Environmental & Water Resources Congress 2010 Providence, Rhode Island – May 17, 2010 Regionalizing StochasticRainfall Generators Dongkyun Kim and Francisco Olivera Zachry Department of Civil Engineering Texas A&M University

  2. Why stochastic rainfall generation? • Synthetic rainfall “data” can be used as input to hydrologic models whenever rainfall data are not available: • Basins with rain gages but with missing data • Basins that need thousands of years of rainfall input to assess the risks associated with hydrologic phenomena (e.g. floods, draughts, water availability, water contamination) • Basins with no rain gages

  3. Storm components • Image Source: http://www.meteoswiss.admin.ch/web/en/research/projects/rain.html

  4. MBLRP model parameters – Storm arrival: Poisson process – Storm duration: Exponential distribution – Rain cell arrival: Poisson process • – Rain cell intensity: Exponential distribution , - Gamma distribution – Rain cell duration: Exponential distribution

  5. MBLRP model parameters • λ (1/T): expected number of storms per unit time. • / (T): expected rain cell duration. • : uniformity of the rain cell durations. • (L/T): expected rain cell intensity. • : ratio of the expected rain cell duration to the expected duration of storm activity. • : product of the expected number of rain cells per unit time times the expected rain cell duration. • For the convenience, the parameters are normalized as  = / and  = /. • Therefore, the following six parameters are typically used: , , , ,  and . • The model calibration consists of minimizing the discrepancy between the statistics of observed and simulated precipitation.

  6. Rainfall statistics Mean_1 Var_1 AC_1 Prob0_1 Mean_3 Var_3 AC_3 Prob0_3 Mean_12 Var_12 AC_12 Prob0_12 Mean_24 Var_24 AC_24 Prob0_24

  7. Rainfall statistics Mean Variance Prob0 Lag-1 autocorrelation

  8. Regionalization • Estimate the MBLRP parameters at 3,444 NCDC gages across the contiguous US. • Interpolate the parameters using the Ordinary Kriging technique. • Cross-validate the parameter maps at all 3,444 gages.

  9. Regionalization - Interpolation • Ordinary Kriging was used to interpolate the estimated parameters • zi = a1*w1 + a2*w2 + a3*w3 + … + an * wn • The weights wi are determined based on a empirically driven function called “variogram.”

  10. Expected Results Expected number of storms per hour in September:  (1/hr)

  11. Regionalization - Multimodality 2 2.8 2 2.3 Number of rain cells 6 15 2 2

  12. Regionalization - Multimodality

  13. Results 72 maps = 6 parameters  12 months

  14. (1/hr)  (hr) •  (mm/hr) •   May

  15. Rainfall Characteristics • Rainfall characteristics according to the MBLRP model:

  16. Average number of rain cells per storm • Average rain cell arrival rate (1/hr) May • Average storm duration (hr) • Average rainfall depth per storm (mm) • Average rain cell duration (hr).

  17. Averagerainfall characteristics for the month of May for selected locations with mean monthly rainfall depth of 141 mm

  18. Validation Cross-validated parameters were used to simulate the accuracy of interpolated points.

  19. Validation

  20. Validation

  21. Summary and Conclusions • 72 MBLRP parameter maps were developed for the contiguous US (i.e., 6 parameters  12 months). • Overall, the parameters showed a regional and seasonal variability: • Strong : λ , μ • Discernible : φ, κ, α • Weak: ν • Parameter values from the maps were cross-validation and showed that the rainfall statistics could be reproduced reasonably well except for the lag-1 autocorrelation coefficient.

  22. Questions?

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